Dynamics of liquid imbibition through paper fibers with intra-pores

The accurate control of liquid imbibition in paper is crucial for the applications of paper to microfluidic devices. However, the classical model for capillary flow in porous media, Lucas-Washburn law, has limitations in predicting the flow in a complex fiber network such as paper. We here report that intra-fiber pores in paper are mainly responsible for the limited accuracy of the previous model. From our experiment, we observed that liquid may imbibe through intra-pores in cellulose fibers as through the pores formed by fiber network. We experimentally measured the flow rate through the intra-pores and theoretically developed a hydrodynamic model for liquid imbibition through paper fibers with intra-pores. Our theoretical predictions are shown to agree well with experimental observations, leading to the physical reasons behind the limits of Lucas-Washburn law.